Problem: $ B = \left[\begin{array}{r}4 \\ 0 \\ -1\end{array}\right]$ $ C = \left[\begin{array}{rrr}4 & -1 & -2 \\ 3 & 1 & 4 \\ -1 & 1 & 3\end{array}\right]$ Is $ B+ C$ defined?
Answer: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ C$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ C$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ C$ Do $ B$ and $ C$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ C$ have the same number of columns? No Yes No No Since $ B$ has different dimensions $(3\times1)$ from $ C$ $(3\times3)$, $ B+ C$ is not defined.